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Latin squares over Abelian groups. (English. Russian original) Zbl 1146.05011
J. Math. Sci., New York 149, No. 3, 1230-1234 (2008); translation from Fundam. Prikl. Mat. 12, No. 3, 65-71 (2006).
Summary: In this paper, parametric families of Latin squares over Boolean vectors and prime fields constructed earlier are generalized to the case of Abelian groups. Some criteria for realizability of this construction are presented. Some classification results are also given.

MSC:
05B15 Orthogonal arrays, Latin squares, Room squares
20K01 Finite abelian groups
94A24 Coding theorems (Shannon theory)
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References:
[1] J. Dénes and A. Keedwell, Latin Squares and Their Applications, Budapest (1974). · Zbl 0283.05014
[2] V. A. Nosov, ”On construction of classes of Latin squares in the Boolean database,” Intellekt. Sistemy, 4, No. 3–4, 307–320 (1999).
[3] V. A. Nosov, ”Constructing a parametric family of Latin squares in the vector database,” Intellekt. Sistemy, 8, No. 1–4, 517–528 (2004).
[4] V. A. Nosov and A. E. Pankratiev, ”Latin squares over Abelian groups,” in: Mathematical Methods and Applications. Proc. XIV Math. Readings of MGSU (January 28–31, 2005) [in Russian], Moscow (2005), pp. 72–76. · Zbl 1146.05011
[5] C. Shannon, ”Communication theory of secrecy systems,” Bell System Tech. J., 28, No. 4, 656–715 (1949). · Zbl 1200.94005
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